{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "angle=np.linspace(0,2*np.pi,180+1)  #画个圆测试下\n",
    "x1=np.cos(angle)\n",
    "y1=np.sin(angle)\n",
    "plt.axis(\"equal\") #xy轴间距相等\n",
    "plt.plot(x1,y1) \n",
    "plt.plot(0,0,'o')\n",
    "plt.show()\n",
    "#设a=1.2,b=1,画个椭圆试试\n",
    "a=1.2\n",
    "b=1\n",
    "c=np.sqrt(a**2-b**2)\n",
    "r=a*b/np.sqrt(b**2*np.cos(angle)**2+a**2*np.sin(angle)**2)#计算极坐标的r\n",
    "x2=r*np.cos(angle)\n",
    "y2=r*np.sin(angle)\n",
    "plt.axis(\"equal\") #xy轴间距相等\n",
    "plt.plot(x2,y2) \n",
    "plt.plot(-c,0,'o')\n",
    "plt.plot(c,0,'o')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def crosspoint(a,b,angle,c):#求从左侧焦点发出一定角度的射线与椭圆的交点。\n",
    "   # c=np.sqrt(a**2-b**2)\n",
    "    k=np.tan(angle)\n",
    "    \n",
    "    A=b**2+(a*k)**2 #二元一次方程系数A,B,C\n",
    "    B=2*c*(a*k)**2\n",
    "    C=(a*c*k)**2-(a*b)**2\n",
    "    \n",
    "    x1=(-B+np.sqrt(B**2-4*A*C))/(2*A)\n",
    "    x2=(-B-np.sqrt(B**2-4*A*C))/(2*A)\n",
    "    y1=(x1+c)*k\n",
    "    y2=(x2+c)*k\n",
    "    \n",
    "    if (angle<np.pi/2)or(angle>3*np.pi/2):\n",
    "        x=x1\n",
    "        y=y1\n",
    "    else:\n",
    "        x=x2\n",
    "        y=y2\n",
    "    return x,y\n",
    "\n",
    "def ovalTangent(a,b,x0,y0): #求椭圆上一点的切线斜率\n",
    "    k=-(b/a)**2*(x0/y0)\n",
    "    return k\n",
    "\n",
    "def reflectAngle(angle,k): #计算反射射线反射角\n",
    "    reflectangle=-(angle-2*np.arctan(k))\n",
    "    return reflectangle\n",
    "\n",
    "def myIntercept(x0,y0,angle): #计算反射线的截距,和当y=0时，x值\n",
    "    b=y0-x0*np.tan(angle)\n",
    "    x=-b/np.tan(angle)\n",
    "    return b,x\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "angle=np.linspace(0,2*np.pi,9+1)\n",
    "\n",
    "for i in range(len(angle)-2): #len(angle)-2 是为了排除水平的两条射线，0度和180度，因为tan计算会有误\n",
    "    a=1.2\n",
    "    b=1\n",
    "    c=np.sqrt(a**2-b**2)\n",
    "    crossX,crossY=crosspoint(a,b,angle[i+1])\n",
    "    k=ovalTangent(a,b,crossX,crossY)\n",
    "    reflect=reflectAngle(angle[i+1],k)\n",
    "    b,interceptX=myIntercept(crossX,crossY,reflect)\n",
    "\n",
    "    plt.axis(\"equal\") #xy轴间距相等\n",
    "    x=[-c,crossX,interceptX]\n",
    "    y=[0,crossY,0]\n",
    "    plt.plot(x,y,color='blue') \n",
    "    \n",
    "    \n",
    "plt.plot(-c,0,'o')\n",
    "plt.plot(c,0,'o')\n",
    "plt.plot(x2,y2) \n",
    "plt.show()\n",
    "\n",
    "\n",
    "for i in range(len(angle)-2): #len(angle)-2 是为了排除水平的两条射线，0度和180度，因为tan计算会有误\n",
    "    a=1.2\n",
    "    b=1\n",
    "    c=0.5\n",
    "    crossX,crossY=crosspoint2(a,b,angle[i+1])\n",
    "    k=ovalTangent(a,b,crossX,crossY)\n",
    "    reflect=reflectAngle(angle[i+1],k)\n",
    "    b,interceptX=myIntercept(crossX,crossY,reflect)\n",
    "\n",
    "    plt.axis(\"equal\") #xy轴间距相等\n",
    "    x=[-c,crossX,interceptX]\n",
    "    y=[0,crossY,0]\n",
    "    plt.plot(x,y,color='blue') \n",
    "plt.plot(-0.6633249580710799,0,'o')\n",
    "plt.plot(0.6633249580710799,0,'o')\n",
    "plt.plot(x2,y2)     \n",
    "plt.show()\n",
    "\n",
    "for i in range(len(angle)-2): #len(angle)-2 是为了排除水平的两条射线，0度和180度，因为tan计算会有误\n",
    "    a=1.2\n",
    "    b=1\n",
    "    c=0.8\n",
    "    crossX,crossY=crosspoint2(a,b,angle[i+1])\n",
    "    k=ovalTangent(a,b,crossX,crossY)\n",
    "    reflect=reflectAngle(angle[i+1],k)\n",
    "    b,interceptX=myIntercept(crossX,crossY,reflect)\n",
    "\n",
    "    plt.axis(\"equal\") #xy轴间距相等\n",
    "    x=[-c,crossX,interceptX]\n",
    "    y=[0,crossY,0]\n",
    "    plt.plot(x,y,color='blue') \n",
    "plt.plot(-0.6633249580710799,0,'o')\n",
    "plt.plot(0.6633249580710799,0,'o')\n",
    "plt.plot(x2,y2)     \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "def crosspoint(angle,x0,y0,p):#求点发出一定角度的射线与抛物线的交点。\n",
    "    k=np.tan(angle)\n",
    "    b=y0-k*x0\n",
    "    \n",
    "    A=k/(2*p)\n",
    "    B=-1\n",
    "    C=b\n",
    "    \n",
    "    y1=(-B+np.sqrt(B**2-4*A*C))/(2*A)\n",
    "    y2=(-B-np.sqrt(B**2-4*A*C))/(2*A)\n",
    "    if (angle<np.pi): #射线角度0-180度y大于0\n",
    "        if y1>0:\n",
    "            y=y1\n",
    "            x=(y-b)/k\n",
    "        else:\n",
    "            y=y2\n",
    "            x=(y-b)/k\n",
    "    else:\n",
    "        if y1<0:\n",
    "            y=y1\n",
    "            x=(y-b)/k\n",
    "        else:\n",
    "            y=y2\n",
    "            x=(y-b)/k\n",
    "    return x,y\n",
    "\n",
    "def parabolaTangent(p,x0,y0): #计算抛物线改点的切线\n",
    "    k=p/y0\n",
    "    return k\n",
    "\n",
    "def reflectAngle(angle,k): #计算反射射线反射角，好像和椭圆一样，cv大法\n",
    "    reflectangle=-(angle-2*np.arctan(k))\n",
    "    return reflectangle\n",
    "\n",
    "def myIntercept(x0,y0,angle): #计算反射线的截距,和当x=4时，y值\n",
    "    b=y0-x0*np.tan(angle)\n",
    "    y=np.tan(angle)*5+b\n",
    "    return b,y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "angle=np.linspace(0,2*np.pi,9+1)\n",
    "\n",
    "for i in range(len(angle)-2): #len(angle)-2 是为了排除水平的两条射线，0度和180度，因为tan计算会有误\n",
    "    p=1\n",
    "    x0=p/2\n",
    "    y0=0\n",
    "    crossX,crossY=crosspoint(angle[i+1],x0,y0,p)\n",
    "    k=parabolaTangent(p,crossX,crossY)\n",
    "    reflect=reflectAngle(angle[i+1],k)\n",
    "    b,interceptY=myIntercept(crossX,crossY,reflect)\n",
    "    \n",
    "    plt.axis(\"equal\") #xy轴间距相等\n",
    "    x=[x0,crossX,5]\n",
    "    y=[y0,crossY,interceptY]\n",
    "    plt.plot(x,y,color='blue') \n",
    "    \n",
    "p=1    \n",
    "y=np.linspace(-3,3,100)\n",
    "x=y**2/(2*p)\n",
    "plt.axis(\"equal\") #xy轴间距相等\n",
    "plt.plot(x,y) \n",
    "plt.plot(p/2,0,'o')\n",
    "plt.show()\n",
    "\n",
    "angle=np.linspace(0,2*np.pi,9+1)\n",
    "\n",
    "for i in range(len(angle)-2): #len(angle)-2 是为了排除水平的两条射线，0度和180度，因为tan计算会有误\n",
    "    p=1\n",
    "    x0=p\n",
    "    y0=0\n",
    "    crossX,crossY=crosspoint(angle[i+1],x0,y0,p)\n",
    "    k=parabolaTangent(p,crossX,crossY)\n",
    "    reflect=reflectAngle(angle[i+1],k)\n",
    "    b,interceptY=myIntercept(crossX,crossY,reflect)\n",
    "    \n",
    "    plt.axis(\"equal\") #xy轴间距相等\n",
    "    x=[x0,crossX,5]\n",
    "    y=[y0,crossY,interceptY]\n",
    "    plt.plot(x,y,color='blue') \n",
    "    \n",
    "p=1    \n",
    "y=np.linspace(-3,3,100)\n",
    "x=y**2/(2*p)\n",
    "plt.axis(\"equal\") #xy轴间距相等\n",
    "plt.plot(x,y) \n",
    "plt.plot(p/2,0,'o')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
